THE EQUALITY OF MIXED PARTIAL DERIVATIVES UNDER WEAK DIFFERENTIABILITY CONDITIONS

Ettore Minguzzi

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THE EQUALITY OF MIXED PARTIAL DERIVATIVES UNDER WEAK DIFFERENTIABILITY CONDITIONS

机译：弱微分条件下混合偏导数的等式

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We review and develop two little known results on the equality of mixed partial derivatives, which can be considered the best results so far available in their respective domains. The former, due to Mikusinski and his school, deals with equality at a given point, while the latter, due to Tolstov, concerns equality almost everywhere. Applications to differential geometry and General Relativity are commented.

机译：我们对混合偏导数的相等性进行了审查，并得出了两个鲜为人知的结果，可以认为这是迄今为止在各自领域中可获得的最佳结果。前者归功于Mikusinski和他的学校，在某一点上处理平等问题，而后者归功于托尔斯托夫，几乎遍及所有地方。评论了微分几何和广义相对论的应用。

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来源
《Real analysis exchange》 |2015年第1期|81-98|共18页
作者
Ettore Minguzzi;
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作者单位

Dipartimento di Matematica e Informatica 'U. Dini', Universita degli Studi di Firenze, Via S. Marta 3, I-50139 Firenze, Italy;

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原文格式 PDF
正文语种 eng
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关键词
Schwarz's theorem; Fubini's theorem; Lipschitz connections;

机译：Schwarz定理;富比尼定理;Lipschitz连接;

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6. Why less may be more: a mixed methods study of the work and relatedness of ‘weak ties’ in supporting long-term condition self-management [O] . Anne Rogers, Helen Brooks, Ivaylo Vassilev, 1985

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7. The equality of mixed partial derivatives under weak differentiability conditions [O] . Minguzzi, E. 2014

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THE EQUALITY OF MIXED PARTIAL DERIVATIVES UNDER WEAK DIFFERENTIABILITY CONDITIONS

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